docs: def calc_empirical_influence_abc(term_plus,
                                   term_minus,
                                   epsilon):
      """
      Calculates the finite difference, midpoint / slope approximation to the
      empirical influence array needed to compute the approximate boostrap
      confidence (ABC) intervals.
  
      Parameters
      ----------
      term_plus : 2D ndarray.
          Should have one row for each observation. Should have one column for
          each parameter in the parameter vector being estimated. Elements should
          denote the finite difference term that comes from adding a small value
          to the observation corresponding to that elements respective row.
      term_minus : 2D ndarray.
          Should have one row for each observation. Should have one column for
          each parameter in the parameter vector being estimated. Elements should
          denote the finite difference term that comes from subtracting a small
          value to the observation corresponding to that elements respective row.
      epsilon : positive float.
          Should denote the 'very small' value being used to calculate the
          desired finite difference approximations to the various influence
          functions. Should be 'close' to zero.
  
      Returns
      -------
      empirical_influence : 2D ndarray.
          Should have one row for each observation. Should have one column for
          each parameter in the parameter vector being estimated. Elements should
          denote the empirical influence of the associated observation on the
          associated parameter.
  
      References
      ----------
      Efron, Bradley, and Robert J. Tibshirani. An Introduction to the Bootstrap.
          CRC press, 1994. Section 22.6, Equation 22.32.
  
      Notes
      -----
      This function is based off of the code in Efron's original Bootstrap
      library, written in S-plus. It is a finite difference, midpoint or slope
      approximation of Equation 22.32.
      """
      # Calculate the denominator of each row of the second order influence array
      denominator = 2 * epsilon
      # Calculate the empirical influence array.
      empirical_influence = np.zeros(term_plus.shape)
      diff_idx = ~np.isclose(term_plus, term_minus, atol=1e-12, rtol=0)
      if diff_idx.any():
          empirical_influence[diff_idx] =\
              (term_plus[diff_idx] - term_minus[diff_idx]) / denominator
      return empirical_influence